This is just an educated guess, but it might have something to do with the fact that one of the accounts is a paid one and probably for some reason Google gives precedence to that one.
– AlexJan 31 at 10:27

You can try to clear cookies/or login using incognito mode in your browser. If nothing of this helps and order of logins still changes automatically, then it's way of how Google works.
– KosFeb 1 at 11:50